the harmonic will be as in tune as the open string is: its just an even division of the string. Intonation can be adjusted thus (I learnt only a month ago on my jazzmaster, using a mustang bridge, so this should be the same...). You will need an electronic tuner (preferably a Korg dt10/pitchblack or similar; the boss tu-2 is only accurate to 3 cents which is more than adequate for tuning normally but we're talking about minute differences here!), a screwdriver, new strings and a lot of patience!
1. fit new strings and adjust action till you're comfortable
2. tune all the strings as perfectly as possible (break them in a little so they hold their pitch)
3. with each string, fret at 12th and check its tuning (don't hold too hard, or else it will read a little sharp and accuracy is everything!): it SHOULD give exactly the same reading
4. if its too sharp, then the string needs to be 'longer', adjust the saddle accordingly (this is tricky at first, but you soon get the idea of how many turns constitutes a small change in pitch). Vice versa if the note is flat (with my jazzmaster, they were nearly all flat, but I don't know if thats just my guitar as oppose to a standard thing)
5. With mustangs and jazzmasters et al, the tremolo design means the tuning will probably go out whenever you make an adjustment: check it after you make adjustments
6. When this process has been completed, strum a big chord and notice how much fuller, thichker, more powerful it sounds. Now try and stop playing for the next hour.